Interested? You can check out Stopxwatch's instructions below:
1. Root your Kindle Fire HD.
2. Downloaded and install the GoogleServicesFramework.apk
3. Download Vending.apk
4. Using a file explorer app on the Fire with superuser permissions AND the system file permissions set to Read-Write, move Vending.apk to /system/app.
5. Change the permissions of Vending.apk to User - Read/Write, Group - Read, Others - Read
6. Install Vending.apk
7. The Android Market should show up in your Kindle Fire HD apps. Tap on it and follow the steps.
8. Download and install the Play.apk to upgrade the the android market to the current Play market.
However, as Brad Linder of Liliputing points out, rooting your tablet and playing around with the /system/ directory can be a bit risky.
"If anything goes wrong, you could end up with an unbootable tablet — and since the Kindle Fire has a locked bootloader, there's no simple way to restore from a backup or re-install the operating system yet," he explained.
"If that doesn't scare you, all you need to do is download the GoogleServicesFramework, Vending and Play files from stopxwatch's links and follow his steps for installing them. You'll need a file explorer that lets you browse root directories and change read/write permissions. ES File Explorer and Root Explorer are both available from the Amazon Appstore."
XDA Dev member Reverendkjr sounded a similar note of caution.
"Keep in mind that we have no way of restoring the system folder yet, so if anything goes wrong with this process, you may end up bricking your tablet. Just a warning."